// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
# include <cppad/cppad.hpp>

namespace { // BEGIN_EMPTY_NAMESPACE
// ---------------------------------------------------------------------------
bool comp_op_dyn_dyn(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   //
   // AD graph example
   // node[0:4] : p[0], p[1], p[2], p[3], p[4]
   // node_5    : x[0]
   //           : p[0] == p[1]
   //           : p[0] <= p[2]
   //           : p[0] <  p[3]
   //           : p[0] != p[4]
   // y[0]      = p[0]
   std::string json =
      "{\n"
      "   'function_name'  : 'comp_op example',\n"
      "   'op_define_vec'  : [ 4, [\n"
      "       { 'op_code':1, 'name':'comp_eq'            } ,\n"
      "       { 'op_code':2, 'name':'comp_le'            } ,\n"
      "       { 'op_code':3, 'name':'comp_lt'            } ,\n"
      "       { 'op_code':4, 'name':'comp_ne'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 5,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 0, [ ] ],\n"
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 0, 2, [1, 2 ] ] ,\n" // p[0] == p[1]
      "       [ 2, 0, 2, [1, 3 ] ] ,\n" // p[0] <= p[2]
      "       [ 3, 0, 2, [1, 4 ] ] ,\n" // p[0] <  p[3]
      "       [ 4, 0, 2, [1, 5 ] ] ]\n" // p[0] != p[4]
      "   ],\n"
      "   'dependent_vec' : [ 1, [1] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = p[0]
   CppAD::ADFun<double> f;
   f.from_json(json);
   //
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 5;
   //
   // set independent variables and parameters so all comparisons true
   vector<double> x(1), p(5);
   x[0] = 1.0;
   p[0] = 3.0;
   p[1] = p[0];
   p[2] = p[0] + 1.0;
   p[3] = p[0] + 1.0;
   p[4] = p[0] + 1.0;
   //
   // compute y = f(x; p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check that all comparisons are true
   ok &= f.compare_change_number() == 0;
   //
   // case where all the comparisons are false
   p[1] = p[0] - 1.0;
   p[2] = p[0] - 1.0;
   p[3] = p[0] - 1.0;
   p[4] = p[0];
   f.new_dynamic(p);
   y = f.Forward(0, x);
   y = f.Forward(0, x);
   ok &= f.compare_change_number() == 4;
   //
   // -----------------------------------------------------------------------
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   // -----------------------------------------------------------------------
   //
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 5;
   //
   // set independent variables and parameters so all comparisons true
   p[0] = 3.0;
   p[1] = p[0];
   p[2] = p[0] + 1.0;
   p[3] = p[0] + 1.0;
   p[4] = p[0] + 1.0;
   //
   // compute y = f(x)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check that all comparisons are true
   ok &= f.compare_change_number() == 0;
   //
   // case where all the comparisons are false
   p[1] = p[0] - 1.0;
   p[2] = p[0] - 1.0;
   p[3] = p[0] - 1.0;
   p[4] = p[0];
   f.new_dynamic(p);
   y = f.Forward(0, x);
   ok &= f.compare_change_number() == 4;
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool comp_op_var_var(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   //
   // AD graph example
   // node[1:5] : x[0], x[1], x[2], x[3], x[4]
   //           : x[0] == x[1]
   //           : x[0] <= x[2]
   //           : x[0] <  x[3]
   //           : x[0] != x[4]
   // y[0]      = x[0]
   std::string json =
      "{\n"
      "   'function_name'  : 'comp_op example',\n"
      "   'op_define_vec'  : [ 4, [\n"
      "       { 'op_code':1, 'name':'comp_eq'            } ,\n"
      "       { 'op_code':2, 'name':'comp_le'            } ,\n"
      "       { 'op_code':3, 'name':'comp_lt'            } ,\n"
      "       { 'op_code':4, 'name':'comp_ne'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 0,\n"
      "   'n_variable_ind' : 5,\n"
      "   'constant_vec'   : [ 0, [ ] ],\n"
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 0, 2, [1, 2 ] ] ,\n" // x[0] == x[1]
      "       [ 2, 0, 2, [1, 3 ] ] ,\n" // x[0] <= x[2]
      "       [ 3, 0, 2, [1, 4 ] ] ,\n" // x[0] <  x[3]
      "       [ 4, 0, 2, [1, 5 ] ] ]\n" // x[0] != x[4]
      "   ],\n"
      "   'dependent_vec' : [ 1, [1] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = p[0]
   CppAD::ADFun<double> f;
   f.from_json(json);
   //
   ok &= f.Domain() == 5;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 0;
   //
   // set independent variables and parameters so all comparisons true
   vector<double> x(5);
   x[0] = 3.0;
   x[1] = x[0];
   x[2] = x[0] + 1.0;
   x[3] = x[0] + 1.0;
   x[4] = x[0] + 1.0;
   //
   // compute y = f(x)
   vector<double> y = f.Forward(0, x);
   //
   // check that all comparisons are true
   ok &= f.compare_change_number() == 0;
   //
   // case where all the comparisons are false
   x[1] = x[0] - 1.0;
   x[2] = x[0] - 1.0;
   x[3] = x[0] - 1.0;
   x[4] = x[0];
   y = f.Forward(0, x);
   ok &= f.compare_change_number() == 4;
   //
   // -----------------------------------------------------------------------
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   // -----------------------------------------------------------------------
   //
   ok &= f.Domain() == 5;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 0;
   //
   // set independent variables and parameters so all comparisons true
   x[0] = 3.0;
   x[1] = x[0];
   x[2] = x[0] + 1.0;
   x[3] = x[0] + 1.0;
   x[4] = x[0] + 1.0;
   //
   // compute y = f(x)
   y = f.Forward(0, x);
   //
   // check that all comparisons are true
   ok &= f.compare_change_number() == 0;
   //
   // case where all the comparisons are false
   x[1] = x[0] - 1.0;
   x[2] = x[0] - 1.0;
   x[3] = x[0] - 1.0;
   x[4] = x[0];
   y = f.Forward(0, x);
   ok &= f.compare_change_number() == 4;
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool comp_op_dyn_var(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   //
   // AD graph example
   // node_1    : p[0]
   // node[2:5] : x[0], x[1], x[2], x[3]
   //           : p[0] == x[0]
   //           : p[0] <= x[1]
   //           : p[0] <  x[2]
   //           : p[0] != x[3]
   // y[0]      = p[0]
   std::string json =
      "{\n"
      "   'function_name'  : 'comp_op example',\n"
      "   'op_define_vec'  : [ 4, [\n"
      "       { 'op_code':1, 'name':'comp_eq'            } ,\n"
      "       { 'op_code':2, 'name':'comp_le'            } ,\n"
      "       { 'op_code':3, 'name':'comp_lt'            } ,\n"
      "       { 'op_code':4, 'name':'comp_ne'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 4,\n"
      "   'constant_vec'   : [ 0, [ ] ],\n"
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 0, 2, [1, 2 ] ] ,\n" // p[0] == x[0]
      "       [ 2, 0, 2, [1, 3 ] ] ,\n" // p[0] <= x[1]
      "       [ 3, 0, 2, [1, 4 ] ] ,\n" // p[0] <  x[2]
      "       [ 4, 0, 2, [1, 5 ] ] ]\n" // p[0] != x[3]
      "   ],\n"
      "   'dependent_vec' : [ 1, [1] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = p[0]
   CppAD::ADFun<double> f;
   f.from_json(json);
   //
   ok &= f.Domain() == 4;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // set independent variables and parameters so all comparisons true
   vector<double> x(4), p(1);
   p[0] = 3.0;
   x[0] = p[0];
   x[1] = p[0] + 1.0;
   x[2] = p[0] + 1.0;
   x[3] = p[0] + 1.0;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check that all comparisons are true
   ok &= f.compare_change_number() == 0;
   //
   // case where all the comparisons are false
   x[0] = p[0] - 1.0;
   x[1] = p[0] - 1.0;
   x[2] = p[0] - 1.0;
   x[3] = p[0];
   f.new_dynamic(p);
   y = f.Forward(0, x);
   ok &= f.compare_change_number() == 4;
   //
   // -----------------------------------------------------------------------
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   // -----------------------------------------------------------------------
   //
   ok &= f.Domain() == 4;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // set independent variables and parameters so all comparisons true
   p[0] = 3.0;
   x[0] = p[0];
   x[1] = p[0] + 1.0;
   x[2] = p[0] + 1.0;
   x[3] = p[0] + 1.0;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check that all comparisons are true
   ok &= f.compare_change_number() == 0;
   //
   // case where all the comparisons are false
   x[0] = p[0] - 1.0;
   x[1] = p[0] - 1.0;
   x[2] = p[0] - 1.0;
   x[3] = p[0];
   f.new_dynamic(p);
   y = f.Forward(0, x);
   ok &= f.compare_change_number() == 4;
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool comp_op_var_dyn(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   //
   // AD graph example
   // node[1:4] : p[0], p[1], p[2], p[3]
   // node_5    : x[0]
   //           : x[0] == p[0]
   //           : x[0] <= p[1]
   //           : x[0] <  p[2]
   //           : x[0] != p[3]
   // y[0]      = p[0]
   std::string json =
      "{\n"
      "   'function_name'  : 'comp_op example',\n"
      "   'op_define_vec'  : [ 4, [\n"
      "       { 'op_code':1, 'name':'comp_eq'            } ,\n"
      "       { 'op_code':2, 'name':'comp_le'            } ,\n"
      "       { 'op_code':3, 'name':'comp_lt'            } ,\n"
      "       { 'op_code':4, 'name':'comp_ne'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 4,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 0, [ ] ],\n"
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 0, 2, [5, 1 ] ] ,\n" // x[0] == p[0]
      "       [ 2, 0, 2, [5, 2 ] ] ,\n" // x[0] <= p[1]
      "       [ 3, 0, 2, [5, 3 ] ] ,\n" // x[0] <  p[2]
      "       [ 4, 0, 2, [5, 4 ] ] ]\n" // x[0] != p[3]
      "   ],\n"
      "   'dependent_vec' : [ 1, [1] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = p[0]
   CppAD::ADFun<double> f;
   f.from_json(json);
   //
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 4;
   //
   // set independent variables and parameters so all comparisons true
   vector<double> x(1), p(4);
   x[0] = 3.0;
   p[0] = x[0];
   p[1] = x[0] + 1.0;
   p[2] = x[0] + 1.0;
   p[3] = x[0] + 1.0;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check that all comparisons are true
   ok &= f.compare_change_number() == 0;
   //
   // case where all the comparisons are false
   p[0] = x[0] - 1.0;
   p[1] = x[0] - 1.0;
   p[2] = x[0] - 1.0;
   p[3] = x[0];
   f.new_dynamic(p);
   y = f.Forward(0, x);
   ok &= f.compare_change_number() == 4;
   //
   // -----------------------------------------------------------------------
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   // -----------------------------------------------------------------------
   //
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 4;
   //
   // set independent variables and parameters so all comparisons true
   x[0] = 3.0;
   p[0] = x[0];
   p[1] = x[0] + 1.0;
   p[2] = x[0] + 1.0;
   p[3] = x[0] + 1.0;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check that all comparisons are true
   ok &= f.compare_change_number() == 0;
   //
   // case where all the comparisons are false
   p[0] = x[0] - 1.0;
   p[1] = x[0] - 1.0;
   p[2] = x[0] - 1.0;
   p[3] = x[0];
   f.new_dynamic(p);
   y = f.Forward(0, x);
   ok &= f.compare_change_number() == 4;
   //
   return ok;
}
// ===========================================================================
bool acosh_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : acosh(p[0])
   // node_5 : acosh(x[0])
   // node_6 : acosh(c[0])
   // node_7 : acosh(p[0]) + acosh(x[0]) + acosh(c[0])
   // y[0]   = acosh(p[0]) + acosh(x[0]) + acosh(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'acosh_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'acosh', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'              } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ 1.3 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // acosh(p0)
      "       [ 1, 2]                ,\n" // acosh(x0)
      "       [ 1, 3]                ,\n" // acosh(c0)
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // acosh(p0)+acosh(x0)+acosh(c0)
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = acosh(p0) + acosh(x0) + acosh(c0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = 1.3;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 1.1;
   x[0] = 1.2;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = CppAD::acosh(p[0]) + CppAD::acosh(x[0]) + CppAD::acosh(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool log1p_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : log1p(p[0])
   // node_5 : log1p(x[0])
   // node_6 : log1p(c[0])
   // node_7 : log1p(p[0]) + log1p(x[0]) + log1p(c[0])
   // y[0]   = log1p(p[0]) + log1p(x[0]) + log1p(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'log1p_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'log1p', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'               } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ 0.3 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // log1p(p0)
      "       [ 1, 2]                ,\n" // log1p(x0)
      "       [ 1, 3]                ,\n" // log1p(c0)
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // log1p(p0)+log1p(x0)+log1p(c0)
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = log1p(p0) + log1p(x0) + log1p(c0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = 0.3;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = -0.1;
   x[0] = 0.2;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = CppAD::log1p(p[0]) + CppAD::log1p(x[0]) + CppAD::log1p(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool expm1_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : expm1(p[0])
   // node_5 : expm1(x[0])
   // node_6 : expm1(c[0])
   // node_7 : expm1(p[0]) + expm1(x[0]) + expm1(c[0])
   // y[0]   = expm1(p[0]) + expm1(x[0]) + expm1(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'expm1_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'expm1', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'              } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ 0.3 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // expm1(p0)
      "       [ 1, 2]                ,\n" // expm1(x0)
      "       [ 1, 3]                ,\n" // expm1(c0)
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // expm1(p0)+expm1(x0)+expm1(c0)
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = expm1(p0) + expm1(x0) + expm1(c0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = 0.3;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = -0.1;
   x[0] = 0.2;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = CppAD::expm1(p[0]) + CppAD::expm1(x[0]) + CppAD::expm1(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool erfc_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : erfc(p[0])
   // node_5 : erfc(x[0])
   // node_6 : erfc(c[0])
   // node_7 : erfc(p[0]) + erfc(x[0]) + erfc(c[0])
   // y[0]   = erfc(p[0]) + erfc(x[0]) + erfc(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'erfc_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'erfc', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ 0.3 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // erfc(p0)
      "       [ 1, 2]                ,\n" // erfc(x0)
      "       [ 1, 3]                ,\n" // erfc(c0)
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // erfc(p0)+erfc(x0)+erfc(c0)
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = erfc(p0) + erfc(x0) + erfc(c0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = 0.3;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = -0.1;
   x[0] = 0.2;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = CppAD::erfc(p[0]) + CppAD::erfc(x[0]) + CppAD::erfc(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool erf_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : erf(p[0])
   // node_5 : erf(x[0])
   // node_6 : erf(c[0])
   // node_7 : erf(p[0]) + erf(x[0]) + erf(c[0])
   // y[0]   = erf(p[0]) + erf(x[0]) + erf(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'erf_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'erf', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ 0.3 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // erf(p0)
      "       [ 1, 2]                ,\n" // erf(x0)
      "       [ 1, 3]                ,\n" // erf(c0)
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // erf(p0)+erf(x0)+erf(c0)
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = erf(p0) + erf(x0) + erf(c0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = 0.3;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = -0.1;
   x[0] = 0.2;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = CppAD::erf(p[0]) + CppAD::erf(x[0]) + CppAD::erf(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool atanh_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : atanh(p[0])
   // node_5 : atanh(x[0])
   // node_6 : atanh(c[0])
   // node_7 : atanh(p[0]) + atanh(x[0]) + atanh(c[0])
   // y[0]   = atanh(p[0]) + atanh(x[0]) + atanh(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'atanh_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'atanh', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'              } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ 0.3 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // atanh(p0)
      "       [ 1, 2]                ,\n" // atanh(x0)
      "       [ 1, 3]                ,\n" // atanh(c0)
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // atanh(p0)+atanh(x0)+atanh(c0)
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = atanh(p0) + atanh(x0) + atanh(c0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = 0.3;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = -0.1;
   x[0] = 0.2;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = CppAD::atanh(p[0]) + CppAD::atanh(x[0]) + CppAD::atanh(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool asinh_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : asinh(p[0])
   // node_5 : asinh(x[0])
   // node_6 : asinh(c[0])
   // node_7 : asinh(p[0]) + asinh(x[0]) + asinh(c[0])
   // y[0]   = asinh(p[0]) + asinh(x[0]) + asinh(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'asinh_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'asinh', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'              } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ 0.3 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // asinh(p0)
      "       [ 1, 2]                ,\n" // asinh(x0)
      "       [ 1, 3]                ,\n" // asinh(c0)
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // asinh(p0)+asinh(x0)+asinh(c0)
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = asinh(p0) + asinh(x0) + asinh(c0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = 0.3;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = -0.1;
   x[0] = 0.2;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = CppAD::asinh(p[0]) + CppAD::asinh(x[0]) + CppAD::asinh(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ===========================================================================
bool tan_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : tan(p[0])
   // node_5 : tan(x[0])
   // node_6 : tan(c[0])
   // node_7 : tan(p[0]) + tan(x[0]) + tan(c[0])
   // y[0]   = tan(p[0]) + tan(x[0]) + tan(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'tan_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'tan', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // tan(p[0])
      "       [ 1, 2]                ,\n" // tan(x[0])
      "       [ 1, 3]                ,\n" // tan(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // tan(p[0])+tan(x[0])+tan(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = tan(p_0) + tan(x_0) + tan(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant that is in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::tan(p[0]) + std::tan(x[0]) + std::tan(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool tanh_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : tanh(p[0])
   // node_5 : tanh(x[0])
   // node_6 : tanh(c[0])
   // node_7 : tanh(p[0]) + tanh(x[0]) + tanh(c[0])
   // y[0]   = tanh(p[0]) + tanh(x[0]) + tanh(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'tanh_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'tanh', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // tanh(p[0])
      "       [ 1, 2]                ,\n" // tanh(x[0])
      "       [ 1, 3]                ,\n" // tanh(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // tanh(p[0])+tanh(x[0])+tanh(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = tanh(p_0) + tanh(x_0) + tanh(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::tanh(p[0]) + std::tanh(x[0]) + std::tanh(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool sqrt_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : sqrt(p[0])
   // node_5 : sqrt(x[0])
   // node_6 : sqrt(c[0])
   // node_7 : sqrt(p[0]) + sqrt(x[0]) + sqrt(c[0])
   // y[0]   = sqrt(p[0]) + sqrt(x[0]) + sqrt(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'sqrt_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'sqrt', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ +0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // sqrt(p[0])
      "       [ 1, 2]                ,\n" // sqrt(x[0])
      "       [ 1, 3]                ,\n" // sqrt(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // sqrt(p[0])+sqrt(x[0])+sqrt(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = sqrt(p_0) + sqrt(x_0) + sqrt(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = +0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::sqrt(p[0]) + std::sqrt(x[0]) + std::sqrt(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool sin_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : sin(p[0])
   // node_5 : sin(x[0])
   // node_6 : sin(c[0])
   // node_7 : sin(p[0]) + sin(x[0]) + sin(c[0])
   // y[0]   = sin(p[0]) + sin(x[0]) + sin(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'sin_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'sin', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // sin(p[0])
      "       [ 1, 2]                ,\n" // sin(x[0])
      "       [ 1, 3]                ,\n" // sin(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // sin(p[0])+sin(x[0])+sin(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = sin(p_0) + sin(x_0) + sin(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::sin(p[0]) + std::sin(x[0]) + std::sin(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool sinh_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : sinh(p[0])
   // node_5 : sinh(x[0])
   // node_6 : sinh(c[0])
   // node_7 : sinh(p[0]) + sinh(x[0]) + sinh(c[0])
   // y[0]   = sinh(p[0]) + sinh(x[0]) + sinh(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'sinh_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'sinh', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // sinh(p[0])
      "       [ 1, 2]                ,\n" // sinh(x[0])
      "       [ 1, 3]                ,\n" // sinh(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // sinh(p[0])+sinh(x[0])+sinh(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = sinh(p_0) + sinh(x_0) + sinh(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::sinh(p[0]) + std::sinh(x[0]) + std::sinh(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool sign_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : sign(p[0])
   // node_5 : sign(x[0])
   // node_6 : sign(c[0])
   // node_7 : sign(p[0]) + sign(x[0]) + sign(c[0])
   // y[0]   = sign(p[0]) + sign(x[0]) + sign(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'sign_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'sign', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // sign(p[0])
      "       [ 1, 2]                ,\n" // sign(x[0])
      "       [ 1, 3]                ,\n" // sign(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // sign(p[0])+sign(x[0])+sign(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = sign(p_0) + sign(x_0) + sign(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = CppAD::sign(p[0]) + CppAD::sign(x[0]) + CppAD::sign(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool log_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : log(p[0])
   // node_5 : log(x[0])
   // node_6 : log(c[0])
   // node_7 : log(p[0]) + log(x[0]) + log(c[0])
   // y[0]   = log(p[0]) + log(x[0]) + log(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'log_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'log', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ +0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // log(p[0])
      "       [ 1, 2]                ,\n" // log(x[0])
      "       [ 1, 3]                ,\n" // log(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // log(p[0])+log(x[0])+log(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = log(p_0) + log(x_0) + log(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = +0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::log(p[0]) + std::log(x[0]) + std::log(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool exp_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : exp(p[0])
   // node_5 : exp(x[0])
   // node_6 : exp(c[0])
   // node_7 : exp(p[0]) + exp(x[0]) + exp(c[0])
   // y[0]   = exp(p[0]) + exp(x[0]) + exp(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'exp_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'exp', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // exp(p[0])
      "       [ 1, 2]                ,\n" // exp(x[0])
      "       [ 1, 3]                ,\n" // exp(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // exp(p[0])+exp(x[0])+exp(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = exp(p_0) + exp(x_0) + exp(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::exp(p[0]) + std::exp(x[0]) + std::exp(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool cos_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : cos(p[0])
   // node_5 : cos(x[0])
   // node_6 : cos(c[0])
   // node_7 : cos(p[0]) + cos(x[0]) + cos(c[0])
   // y[0]   = cos(p[0]) + cos(x[0]) + cos(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'cos_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'cos', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // cos(p[0])
      "       [ 1, 2]                ,\n" // cos(x[0])
      "       [ 1, 3]                ,\n" // cos(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // cos(p[0])+cos(x[0])+cos(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = cos(p_0) + cos(x_0) + cos(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::cos(p[0]) + std::cos(x[0]) + std::cos(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool cosh_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : cosh(p[0])
   // node_5 : cosh(x[0])
   // node_6 : cosh(c[0])
   // node_7 : cosh(p[0]) + cosh(x[0]) + cosh(c[0])
   // y[0]   = cosh(p[0]) + cosh(x[0]) + cosh(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'cosh_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'cosh', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // cosh(p[0])
      "       [ 1, 2]                ,\n" // cosh(x[0])
      "       [ 1, 3]                ,\n" // cosh(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // cosh(p[0])+cosh(x[0])+cosh(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = cosh(p_0) + cosh(x_0) + cosh(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::cosh(p[0]) + std::cosh(x[0]) + std::cosh(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool atan_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : atan(p[0])
   // node_5 : atan(x[0])
   // node_6 : atan(c[0])
   // node_7 : atan(p[0]) + atan(x[0]) + atan(c[0])
   // y[0]   = atan(p[0]) + atan(x[0]) + atan(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'atan_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'atan', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // atan(p[0])
      "       [ 1, 2]                ,\n" // atan(x[0])
      "       [ 1, 3]                ,\n" // atan(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // atan(p[0])+atan(x[0])+atan(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = atan(p_0) + atan(x_0) + atan(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::atan(p[0]) + std::atan(x[0]) + std::atan(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool asin_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : asin(p[0])
   // node_5 : asin(x[0])
   // node_6 : asin(c[0])
   // node_7 : asin(p[0]) + asin(x[0]) + asin(c[0])
   // y[0]   = asin(p[0]) + asin(x[0]) + asin(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'asin_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'asin', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // asin(p[0])
      "       [ 1, 2]                ,\n" // asin(x[0])
      "       [ 1, 3]                ,\n" // asin(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // asin(p[0])+asin(x[0])+asin(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = asin(p_0) + asin(x_0) + asin(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::asin(p[0]) + std::asin(x[0]) + std::asin(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool acos_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : acos(p[0])
   // node_5 : acos(x[0])
   // node_6 : acos(c[0])
   // node_7 : acos(p[0]) + acos(x[0]) + acos(c[0])
   // y[0]   = acos(p[0]) + acos(x[0]) + acos(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'acos_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'acos', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'             } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // acos(p[0])
      "       [ 1, 2]                ,\n" // acos(x[0])
      "       [ 1, 3]                ,\n" // acos(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // acos(p[0])+acos(x[0])+acos(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = acos(p_0) + acos(x_0) + acos(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::acos(p[0]) + std::acos(x[0]) + std::acos(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
bool abs_op(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   //
   // AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : c[0]
   // node_4 : abs(p[0])
   // node_5 : abs(x[0])
   // node_6 : abs(c[0])
   // node_7 : abs(p[0]) + abs(x[0]) + abs(c[0])
   // y[0]   = abs(p[0]) + abs(x[0]) + abs(c[0])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'abs_op example',\n"
      "   'op_define_vec'  : [ 2, [\n"
      "       { 'op_code':1, 'name':'abs', 'n_arg':1 } ,\n"
      "       { 'op_code':2, 'name':'sum'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 1, [ -0.1 ] ],\n" // c[0]
      "   'op_usage_vec'   : [ 4, [\n"
      "       [ 1, 1]                ,\n" // abs(p[0])
      "       [ 1, 2]                ,\n" // abs(x[0])
      "       [ 1, 3]                ,\n" // abs(c[0])
      "       [ 2, 1, 3, [4, 5, 6] ] ]\n" // abs(p[0])+abs(x[0])+abs(c[0])
      "   ],\n"
      "   'dependent_vec' : [ 1, [7] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   // f(x, p) = abs(p_0) + abs(x_0) + abs(c_0)
   CppAD::ADFun<double> f;
   f.from_json(json);
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 1;
   //
   // value of constant in function
   vector<double> c(1);
   c[0] = -0.1;
   //
   // set independent variables and parameters
   vector<double> p(1), x(1);
   p[0] = 0.2;
   x[0] = 0.3;
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   vector<double> y = f.Forward(0, x);
   //
   // check result
   double check = std::fabs(p[0]) + std::fabs(x[0]) + std::fabs(c[0]);
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   // Convert to Json graph and back again
   json = f.to_json();
   // std::cout << graph;
   f.from_json(json);
   //
   // compute y = f(x, p)
   f.new_dynamic(p);
   y = f.Forward(0, x);
   //
   // check result
   ok &= CppAD::NearEqual(y[0], check, eps99, eps99);
   //
   return ok;
}
// ---------------------------------------------------------------------------
// Test conditonal expression
bool cexp_lt_variable(void)
{  bool ok = true;
   using CppAD::vector;
   //
   // An AD graph example
   // node_1 : x[0]
   // node_2 : x[1]
   // node_3 : cexp_lt(x[0], x[1], x[1], x[0])
   // y[0]   = max(x[0], x[1])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'cexp_lt test',\n"
      "   'op_define_vec'  : [ 1, [\n"
      "       { 'op_code':1, 'name':'cexp_lt', 'n_arg':4 } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 0,\n"
      "   'n_variable_ind' : 2,\n"
      "   'constant_vec'   : [ 0, [] ],\n"
      "   'op_usage_vec'   : [ 1, [\n"
      "       [ 1, 1, 2, 2, 1 ] ] \n"
      "   ],\n"
      "   'dependent_vec'   : [ 1, [3] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   CppAD::ADFun<double> f;
   f.from_json(json);
   // ---------------------------------------------------------------------
   ok &= f.Domain() == 2;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 0;
   //
   vector<double> x(2), y(1);
   x[0] = 2.0;
   x[1] = 3.0;
   y = f.Forward(0, x);
   ok &= y[0] == std::max(x[0], x[1]);
   //
   x[0] = 3.0;
   x[1] = 2.0;
   y = f.Forward(0, x);
   ok &= y[0] == std::max(x[0], x[1]);
   // ---------------------------------------------------------------------
   json = f.to_json();
   f.from_json(json);
   // ---------------------------------------------------------------------
   ok &= f.Domain() == 2;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 0;
   //
   x[0] = 2.0;
   x[1] = 3.0;
   y = f.Forward(0, x);
   ok &= y[0] == std::max(x[0], x[1]);
   //
   x[0] = 3.0;
   x[1] = 2.0;
   y = f.Forward(0, x);
   ok &= y[0] == std::max(x[0], x[1]);
   //
   // std::cout << graph;
   return ok;
}
// Test conditonal expression
bool cexp_lt_constant(void)
{  bool ok = true;
   using CppAD::vector;
   //
   // An AD graph example
   // node_1 : x[0]
   // node_2 : c[0]
   // node_3 : c[1]
   // node_4 : cexp_lt(c[0], c[1], c[1], c[0])
   // y[0]   = max(c[0], c[1])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'cexp_lt test',\n"
      "   'op_define_vec'  : [ 1, [\n"
      "       { 'op_code':1, 'name':'cexp_lt', 'n_arg':4 } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 0,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 2, [ 5.0, -5.0 ] ],\n"
      "   'op_usage_vec'   : [ 1, [\n"
      "       [ 1, 2, 3,  3, 2 ] ] \n"
      "   ],\n"
      "   'dependent_vec'   : [ 1, [4] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   CppAD::ADFun<double> f;
   f.from_json(json);
   // ---------------------------------------------------------------------
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 0;
   //
   vector<double> c(2), x(1), y(1);
   c[0] = 5.0;
   c[1] = -5.0;
   y = f.Forward(0, x);
   ok &= y[0] == std::max(c[0], c[1]);
   // ---------------------------------------------------------------------
   json = f.to_json();
   f.from_json(json);
   // ---------------------------------------------------------------------
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 0;
   //
   ok &= y[0] == std::max(c[0], c[1]);
   // ---------------------------------------------------------------------
   // std::cout << graph;
   return ok;
}
bool cexp_lt_dynamic(void)
{  bool ok = true;
   using CppAD::vector;
   //
   // An AD graph example
   // node_1 : p[0]
   // node_2 : p[1]
   // node_3 : x[0]
   // node_4 : cexp_lt(p[0], p[1], p[1], p[0])
   // y[0]   = max(p[0], p[1])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'cexp_lt test',\n"
      "   'op_define_vec'  : [ 1, [\n"
      "       { 'op_code':1, 'name':'cexp_lt', 'n_arg':4 } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 2,\n"
      "   'n_variable_ind' : 1,\n"
      "   'constant_vec'   : [ 0, [ ] ],\n"
      "   'op_usage_vec'   : [ 1, [\n"
      "       [ 1, 1, 2, 2, 1 ] ] \n"
      "   ],\n"
      "   'dependent_vec'   : [ 1, [4] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   CppAD::ADFun<double> f;
   f.from_json(json);
   // ---------------------------------------------------------------------
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 2;
   //
   vector<double> p(2), x(1), y(1);
   p[0] = 3.0;
   p[1] = 2.0;
   f.new_dynamic(p);
   y = f.Forward(0, x);
   ok &= y[0] == std::max(p[0], p[1]);
   // ---------------------------------------------------------------------
   json = f.to_json();
   // std::cout << graph;
   f.from_json(json);
   // ---------------------------------------------------------------------
   ok &= f.Domain() == 1;
   ok &= f.Range() == 1;
   ok &= f.size_dyn_ind() == 2;
   //
   p[0] = 2.0;
   p[1] = 3.0;
   f.new_dynamic(p);
   y = f.Forward(0, x);
   ok &= y[0] == std::max(p[0], p[1]);
   // ---------------------------------------------------------------------
   // std::cout << graph;
   return ok;
}
// ---------------------------------------------------------------------------
// Test atomic function that gets passed both variables and dynamic parameters
bool atomic_both(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   //
   // y[0] = p[0] * x[0]
   vector< AD<double> > ap(1), ax(1), ay(1);
   ap[0] = 2.0;
   ax[0] = 3.0;
   size_t abort_op_index = 0;
   bool   record_compare = false;
   CppAD::Independent(ax, abort_op_index, record_compare, ap);
   ay[0] = ap[0] * ax[0];
   CppAD::ADFun<double> f(ax, ay);
   //
   // Create a ckhpoint_two with name f(x; p).
   // (This also creates an atomic_three fucntion with same name.)
   bool internal_bool    = false;
   bool use_hes_sparsity = false;
   bool use_base2ad      = false;
   bool use_in_parallel  = false;
   CppAD::chkpoint_two<double> chk_f(f, "f(x; p)",
      internal_bool, use_hes_sparsity, use_base2ad, use_in_parallel
   );
   // -----------------------------------------------------------------------
   // g(u; p)
   vector< AD<double> > au(2), av(1);
   au[0] = 5.0;
   au[1] = 6.0;
   CppAD::Independent(au);
   ax[0] = au[0];
   chk_f(ax, av);          // v[0] = p[0] * u[0]
   ay[0] = au[1] + av[0];  // y[0] = u[1] + p[0] * u[0]
   CppAD::ADFun<double> g(au, ay);
   // ---------------------------------------------------------------------
   ok &= g.Domain() == 2;
   ok &= g.Range() == 1;
   ok &= g.size_dyn_ind() == 0;
   //
   // evalute g(u; p)
   vector<double> p(1), u(2), y(1);
   p[0] = 3.0;
   u[0] = 4.0;
   u[1] = 5.0;
   chk_f.new_dynamic(p);
   y    = g.Forward(0, u);
   //
   // check value
   double check = u[1] + p[0] * u[0];
   ok &= y[0] == check;
   // ---------------------------------------------------------------------
   std::string json = g.to_json();
   // std::cout << json;
   g.from_json(json);
   // ---------------------------------------------------------------------
   ok &= g.Domain() == 2;
   ok &= g.Range() == 1;
   ok &= g.size_dyn_ind() == 0;
   //
   // evalute g(u; p)
   p[0] = 4.0;
   u[0] = 5.0;
   u[1] = 6.0;
   chk_f.new_dynamic(p);
   y    = g.Forward(0, u);
   //
   // check value
   check = u[1] + p[0] * u[0];
   ok &= y[0] == check;

   // -----------------------------------------------------------------------
   // std::cout << graph;
   return ok;
}
// ---------------------------------------------------------------------------
// Test atomic function that only gets passed dynamic parameters
bool atomic_dynamic(void)
{  bool ok = true;
   using CppAD::vector;
   using CppAD::AD;
   //
   // y[0] = x[0] * x[1]
   vector< AD<double> > ax(2), ay(1);
   ax[0] = 2.0;
   ax[1] = 3.0;
   CppAD::Independent(ax);
   ay[0] = ax[0] * ax[1];
   CppAD::ADFun<double> f(ax, ay);
   //
   // Create a ckhpoint_two with name f(x).
   // (This also creates an atomic_three fucntion with same name.)
   bool internal_bool    = false;
   bool use_hes_sparsity = false;
   bool use_base2ad      = false;
   bool use_in_parallel  = false;
   CppAD::chkpoint_two<double> chk_f(f, "f(x)",
      internal_bool, use_hes_sparsity, use_base2ad, use_in_parallel
   );
   // -----------------------------------------------------------------------
   vector< AD<double> > au(1), aq(2), av(1);
   aq[0] = 4.0;
   aq[1] = 5.0;
   au[0] = 6.0;
   size_t abort_op_index = 0;
   bool   record_compare = false;
   CppAD::Independent(au, abort_op_index, record_compare, aq);
   chk_f(aq, av);          // v[0] = q[0] * q[1]
   ay[0] = au[0] + av[0];  // y[0] = u[0] + q[0] * q[1]
   CppAD::ADFun<double> g(au, ay);
   //
   // ---------------------------------------------------------------------
   ok &= g.Domain() == 1;
   ok &= g.Range() == 1;
   ok &= g.size_dyn_ind() == 2;
   //
   // set q in g(u; q)
   vector<double> q(2);
   q[0] = 2.0;
   q[1] = 3.0;
   g.new_dynamic(q);
   //
   // evalute g(u; q)
   vector<double> u(1), y(1);
   u[0] = 4.0;
   y    = g.Forward(0, u);
   //
   // check value
   double check = u[0] + q[0] * q[1];
   ok &= y[0] == check;
   // ---------------------------------------------------------------------
   std::string json = g.to_json();
   // std::cout << graph;
   g.from_json(json);
   //
   ok &= g.Domain() == 1;
   ok &= g.Range() == 1;
   ok &= g.size_dyn_ind() == 2;
   //
   // set q in g(u; q)
   q[0] = 3.0;
   q[1] = 4.0;
   g.new_dynamic(q);
   //
   // evalute g(u; q)
   u[0] = 5.0;
   y    = g.Forward(0, u);
   //
   // check value
   check = u[0] + q[0] * q[1];
   ok &= y[0] == check;
   // ----------------------------------------------------------------------
   // std::cout << graph;
   return ok;
}
// ---------------------------------------------------------------------------
// Test transforming to Json and back to a function
bool to_json_and_back(void)
{  bool ok = true;
   using CppAD::vector;
   //
   // An AD graph example
   // node_1 : p[0]
   // node_2 : x[0]
   // node_3 : x[1]
   // node_4 : -2.0
   // node_5 : p[0] + x[0] + x[1]
   // node_6 : (p[0] + x[0] + x[1]) * (p[0] + x[0] + x[1])
   // y[0]   = (p[0] + x[0] + x[1]) * (p[0] + x[0] + x[1])
   // use single quote to avoid having to escape double quote
   std::string json =
      "{\n"
      "   'function_name'  : 'to_json_and_back test',\n"
      "   'op_define_vec'  : [ 3, [\n"
      "       { 'op_code':1, 'name':'add', 'n_arg':2 } ,\n"
      "       { 'op_code':2, 'name':'mul', 'n_arg':2 } ,\n"
      "       { 'op_code':3, 'name':'sum'            } ]\n"
      "   ],\n"
      "   'n_dynamic_ind'  : 1,\n"
      "   'n_variable_ind' : 2,\n"
      "   'constant_vec'   : [ 1, [ -2.0 ] ],\n"
      "   'op_usage_vec'   : [ 2, [\n"
      "       [ 3, 1, 3, [1, 2, 3 ] ] ,\n"
      "       [ 2, 5, 5             ] ] \n"
      "   ],\n"
      "   'dependent_vec'   : [ 1, [6] ] \n"
      "}\n";
   // Convert the single quote to double quote
   for(size_t i = 0; i < json.size(); ++i)
      if( json[i] == '\'' ) json[i] = '"';
   //
   CppAD::ADFun<double> fun;
   fun.from_json(json);
   json = fun.to_json();
   // For debugging
   // std::cout << "json = " << json;
   fun.from_json(json);
   //
   // Compute function value
   vector<double> p(1), x(2);
   p[0] = 1.0;
   x[0] = 2.0;
   x[1] = 3.0;
   fun.new_dynamic(p);
   vector<double> y = fun.Forward(0, x);
   ok  &= y[0] ==  (p[0] + x[0] + x[1]) * (p[0] + x[0] + x[1]);
   //
   // Conpute derivative value
   vector<double> jac = fun.Jacobian(x);
   ok &= jac[0] == 2.0 * (p[0] + x[0] + x[1]);
   ok &= jac[1] == 2.0 * (p[0] + x[0] + x[1]);
   //
   // Uncomment statement below to see the graph
   // std::cout << graph;
   //
   return ok;
}
// ---------------------------------------------------------------------------
// Test binary operators that should be implemented
bool binary_operators(void)
{  bool ok   = true;
   using CppAD::AD;
   //
   size_t np = 1;
   size_t nx = 2;
   size_t ny = 10;
   CPPAD_TESTVECTOR(double)       p(np),   x(nx);
   CPPAD_TESTVECTOR( AD<double> ) ap(np), ax(nx), ay(ny);
   for(size_t i = 0; i < np; ++i)
   {  ap[i] = 0.5;
      p[i]  = double(i + 1);
   }
   for(size_t i = 0; i < nx; ++i)
   {  ax[i] = 0.25;
      x[i]  = double(2 * i + 1);
   }
   CppAD::Independent(ax, ap);
   //
   size_t j = 0;
   ay[j++] = ap[0] + 2.0;    // dynamic + constant (and ParOp)
   ay[j++] = 2.0 + ap[0];    // constant + dynamic (and ParOp)
   ay[j++] = ax[0] + ap[0];  // variable + dynamic
   ay[j++] = ap[0] + ax[0];  // dynamic + variable
   ay[j++] = ax[0] + ax[1];  // variable + variable
   //
   ay[j++] = ap[0] * 2.0;    // dynamic * constant (and ParOp)
   ay[j++] = 2.0 * ap[0];    // constant * dynamic (and ParOp)
   ay[j++] = ax[0] * ap[0];  // variable * dynamic
   ay[j++] = ap[0] * ax[0];  // dynamic * variable
   ay[j++] = ax[0] * ax[1];  // variable * variable
   //
   ok &= j == ny;
   //
   // Create function
   CppAD::ADFun<double> f(ax, ay);
   //
   // Evaluate function at x before
   f.new_dynamic(p);
   CPPAD_TESTVECTOR(double) y_before = f.Forward(0, x);
   //
   // Convert to Json and back again
   std::string json = f.to_json();
   // std::cout << graph;
   f.from_json(json);
   //
   // Evaluate function at x after
   f.new_dynamic(p);
   CPPAD_TESTVECTOR(double) y_after = f.Forward(0, x);
   //
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   for(size_t i = 0; i < ny; ++i)
      ok &= CppAD::NearEqual( y_before[i], y_after[i], eps99, eps99 );
   //
   // Uncomment statement below to see the graph
   // std::cout << graph;
   return ok;
}
// ---------------------------------------------------------------------------
// Test cumulative sum operator
bool cumulative_sum(void)
{  bool ok   = true;
   using CppAD::AD;
   //
   size_t np = 2;
   size_t nx = 2;
   size_t ny = 1;
   CPPAD_TESTVECTOR(double)       p(np),   x(nx);
   CPPAD_TESTVECTOR( AD<double> ) ap(np), ax(nx), ay(ny);
   for(size_t i = 0; i < np; ++i)
   {  ap[i] = 0.5;
      p[i]  = double(i + 1);
   }
   for(size_t i = 0; i < nx; ++i)
   {  ax[i] = 0.25;
      x[i]  = double(2 * i + 1);
   }
   CppAD::Independent(ax, ap);
   //
   AD<double> asum = 0.0;
   asum +=  1.0 + ap[0];
   asum += ap[1] + 1.0;
   asum -= ap[1] + ap[0];
   //
   asum +=  1.0 + ax[0];
   asum += ax[1] + 1.0;
   asum -= ax[1] + ax[0];
   //
   asum += ap[0] + ax[0];
   asum += ax[1] + ap[1];
   //
   ay[0] = asum;
   //
   // Create function
   CppAD::ADFun<double> f(ax, ay);
   f.optimize();
   //
   // Evaluate function at x before
   f.new_dynamic(p);
   CPPAD_TESTVECTOR(double) y_before = f.Forward(0, x);
   //
   // Convert to Json and back again
   std::string json = f.to_json();
   // std::cout << graph;
   f.from_json(json);
   //
   // Evaluate function at x after
   f.new_dynamic(p);
   CPPAD_TESTVECTOR(double) y_after = f.Forward(0, x);
   //
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   for(size_t i = 0; i < ny; ++i)
      ok &= CppAD::NearEqual( y_before[i], y_after[i], eps99, eps99 );
   //
   // Uncomment statement below to see the graph
   // std::cout << graph;
   return ok;
}
// ---------------------------------------------------------------------------
// Test unary operators
bool unary(bool p_first)
{  bool ok   = true;
   using CppAD::AD;
   //
   size_t np = 11;
   size_t nx = 11;
   size_t ny = np + nx;
   CPPAD_TESTVECTOR(double)       p(np),  x(nx), y(ny);
   CPPAD_TESTVECTOR( AD<double> ) ap(np), ax(nx), ay(ny);
   for(size_t i = 0; i < np; ++i)
   {  p[i]  = double(i + 1) / double( np + nx + 1 );
      ap[i] = p[i] / 2.0;
   }
   for(size_t i = 0; i < nx; ++i)
   {  x[i]  = double(i + 1 + np) / double( np + nx + 1);
      ax[i] = x[i] / 2.0;
   }
   CppAD::Independent(ax, ap);
   //
   CPPAD_TESTVECTOR( AD<double> ) atmp(np + nx);
   if( p_first )
   {  for(size_t i = 0; i < np; ++i)
         atmp[i] = ap[i];
      for(size_t i = 0; i < nx; ++i)
         atmp[i + np] = ax[i];
   }
   else
   {  for(size_t i = 0; i < np; ++i)
         atmp[i + nx] = ap[i];
      for(size_t i = 0; i < nx; ++i)
         atmp[i] = ax[i];
   }
   //
   ay[0]  = fabs(atmp[0]);
   ay[1]  = acos(atmp[1]);
   ay[2]  = acosh(atmp[2] + 1.0);
   ay[3]  = asin(atmp[3]);
   ay[4]  = asinh(atmp[4]);
   ay[5]  = atan(atmp[5]);
   ay[6]  = atanh(atmp[6]);
   ay[7]  = cos(atmp[7]);
   ay[8]  = cosh(atmp[8]);
   ay[9]  = erf(atmp[9]);
   ay[10] = erfc(atmp[10]);
   ay[11] = exp(atmp[11]);
   ay[12] = expm1(atmp[12]);
   ay[13] = log(atmp[13]);
   ay[14] = log1p(atmp[14]);
   ay[15] = - atmp[15];
   ay[16] = sign(atmp[16]);
   ay[17] = sin(atmp[17]);
   ay[18] = sinh(atmp[18]);
   ay[19] = sqrt(atmp[19]);
   ay[20] = tan(atmp[20]);
   ay[21] = sin(atmp[21]);
   // Create function
   CppAD::ADFun<double> f(ax, ay);
   f.optimize();
   //
   // Evaluate function at x before
   f.new_dynamic(p);
   CPPAD_TESTVECTOR(double) y_before = f.Forward(0, x);
   //
   // Convert to Json and back again
   std::string json = f.to_json();
   // std::cout << graph;
   f.from_json(json);
   //
   // Evaluate function at x after
   f.new_dynamic(p);
   CPPAD_TESTVECTOR(double) y_after = f.Forward(0, x);
   //
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();
   for(size_t i = 0; i < ny; ++i)
      ok &= CppAD::NearEqual( y_before[i], y_after[i], eps99, eps99 );
   //
   return ok;
}

// ---------------------------------------------------------------------------
} // END_EMPTY_NAMESPACE


bool json_graph(void)
{  bool ok = true;
   ok     &= comp_op_dyn_dyn();
   ok     &= comp_op_var_var();
   ok     &= comp_op_dyn_var();
   ok     &= comp_op_var_dyn();
   ok     &= acosh_op();
   ok     &= log1p_op();
   ok     &= expm1_op();
   ok     &= erfc_op();
   ok     &= erf_op();
   ok     &= atanh_op();
   ok     &= asinh_op();
   ok     &= tan_op();
   ok     &= tanh_op();
   ok     &= sqrt_op();
   ok     &= sin_op();
   ok     &= sinh_op();
   ok     &= sign_op();
   ok     &= log_op();
   ok     &= exp_op();
   ok     &= cos_op();
   ok     &= cosh_op();
   ok     &= atan_op();
   ok     &= asin_op();
   ok     &= acos_op();
   ok     &= abs_op();
   ok     &= cexp_lt_variable();
   ok     &= cexp_lt_constant();
   ok     &= cexp_lt_dynamic();
   ok     &= atomic_both();
   ok     &= atomic_dynamic();
   ok     &= to_json_and_back();
   ok     &= binary_operators();
   ok     &= cumulative_sum();
   ok     &= unary(true);
   ok     &= unary(false);
   //
   return ok;
}
